Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems

被引：28
|
作者：
Ceng, Lu-Chuan [2 ,3 ]
Guu, Sy-Ming [1 ]
Yao, Jen-Chih [4 ]
机构：
[1] Yuan Ze Univ, Dept Business Adm, Coll Management, Chungli 330, Taoyuan Hsien, Taiwan
[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[3] Sci Comp Key Lab Shanghai Univ, Shanghai, Peoples R China
[4] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 807, Taiwan
来源：
FIXED POINT THEORY AND APPLICATIONS | 2012年
基金：
美国国家科学基金会;
关键词：
Generalized mixed equilibrium problem; fixed point; nonexpansive mapping; variational inequality; hybrid iterative method; VISCOSITY APPROXIMATION METHODS; STEEPEST-DESCENT METHODS; NONEXPANSIVE-MAPPINGS; VARIATIONAL-INEQUALITIES; STRONG-CONVERGENCE; EXTRAGRADIENT METHOD; HILBERT-SPACES; FINITE FAMILY; SCHEME; THEOREM;
D O I：
10.1186/1687-1812-2012-92
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of , which is the unique solution of a variational inequality. AMS subject classifications: 49J40; 47J20; 47H09.
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页数：19
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